1. Identifying Congruent Triangles
OBJECTIVES
- Triangle classification by parts
- Angle Sum Theorem & Exterior Angle Theorem
- CPTC,SSS,SAS,ASA,and AAS Theorems
- Problem solving by eliminating possibilities
-Equilateral & Isosceles triangles

2. Classifying triangles
By angle measures
Right one angle 90°
Obtuseone angle obtuse
Acuteall angles acute
equiangularall 3
By side lengths
Equilateral 3 sides
Isosceles 2 sides
Scaleneno lengths same
Parts of an Isosceles Triangle
Vertex Angle
2 sides  leg
leg
Base angle
 Base angle
Base is side opposite vertex

3. Measuring angles in triangles
The sum of the measures of the 3 angles of a triangle always equals 180º
If 2
In a right triangle, the 2 acute angles are complementary
There can be at most 1 obtuse or 1 right angle in a Δ
The measure of an exterior angle = the measure of the two remote interior angles:
Remote interior angles
Exterior angle

4. Congruent triangles: CPCTC
Two Δ’s are congruent if and only if their corresponding parts are congruent (all sides & all angles)
corr parts 1 2
Congruence of triangles is:
reflexive (parts to self) symmetric
transitive

5. If 2 triangles are congruent:1
The congruence statement statement tells which parts of triangle 1 ‘match up’ or correspond to the parts of triangle 2.
Means
ORDER IS VERY IMPORTANT

6. Proving Δ’s congruent: SSS & SAS & ASA
Given: 2 Δ’s (match up sides/angles that are alike)
If 3 sides
2 sides & an included angle 
OR 2 angles & an included side 
are congruent
 THEN the 2 Δ’s are congruent
** remember-- in two column proofs the ‘if’ part matches what you know & goes in the left column. The ‘then’ part goes in the right column & gives direction towards the statement to be proven.

7. Congruent triangles: AAS
‘Read around’ the vertices of a triangle: if an angle & another angle & a side not between them are congruent to the corresponding parts of another triangle,
 THEN the triangles are congruent
Mark the given parts on your triangles to see which theorem or postulate to use. There WILL be a clue to get you started B D F E C A

8. Isosceles triangles If 2 sides are ,  then angles opposite them areB A C
If 2 sides are ,  then angles opposite them are
If 2 angles of a triangle are , then the sides opposite are
A triangle is equilateral if and only if it is equiangular
Each angle of an equiangular triangle measures 60°

9. Example: Given: ΔTEN is an isosceles triangle with base TN1 2 3 4 T C A N
Given: ΔTEN is an isosceles triangle with base TN
Prove: ΔTEA ΔNEC
1. ΔTEN is an isosceles triangle with base TN 1. Given
2.Def Isosceles
3.Given
4. ΔTEA ΔNEC 4.AAS
End with what you are to prove